In the effective field theory framework the interaction between two heavy hadrons can be decomposed into a long- and a short-range piece. The long-range piece corresponds to the one-pion-exchange potential and is relatively well-known. The short-range piece is given by a series of contact-range interactions with unknown couplings, which substitute the less well-known short-range dynamics. While the general structure of the short-range potential between heavy hadrons is heavily constrained from heavy-quark symmetry, the couplings are still free parameters. Here we argue that the relative strength and the sign of these couplings can be estimated from the hypothesis that they are saturated by the exchange of light mesons, in particular the vector mesons $ρ$ and $ω$, i.e. from resonance saturation. However, we propose a novel saturation procedure that effectively removes form-factor artifacts. From this we can determine in which spin and isospin configurations the low-energy constants are most attractive for specific two-heavy-hadron systems. In general the molecular states with lower isospins and higher spins will be more attractive and thus more probable candidates to form heavy-hadron molecules. This pattern is compatible with the interpretation of the $X(3872)$ and $P_c(4312/4440/4457)$ as molecular states, but it is not applicable to states with maximum isospin like the $Z_c(3900/4020)$.
We systematically study exclusive diffractive (photo) production of vector mesons ($J/ψ$, $ψ(2s)$, $ϕ$ and $ρ$) off protons in high-energy collisions and investigate whether the production is a sensitive probe of gluon saturation. We confront saturation-based results for diffractive $ψ(2s)$ and $ρ$ production at HERA and $J/ψ$ photoproduction with all available data including recent ones from HERA, ALICE and LHCb, finding good agreement. In particular, we show that the $t$-distribution of differential cross sections of photoproduction of vector mesons offers a unique opportunity to discriminat…
We compute total and differential elastic cross sections of high-energy hadronic collisions in the loop-loop correlation model that provides a unified description of hadron-hadron, photon-hadron, and photon-photon reactions. The impact parameter profiles of pp and gamma*p collisions are calculated. For ultra-high energies the hadron opacity saturates at the black disc limit which tames the growth of the hadronic cross sections in agreement with the Froissart bound. We compute the impact parameter dependent gluon distribution of the proton xG(x,Q^2,b) and find gluon saturation at small Bjorken …
We argue that gluon saturation effects may be visible in Large Hadron Collider (LHC) data. We look at the centrality dependence of the away-side peak of two-particle correlations measured in p-Pb collisions, using both ALICE data at midrapidity, and LHCb data at forward rapidity. Once the collective flow-like signal measured at the near-side peak is removed from the correlation function, the centrality dependence of the away-side peak turns out to be much stronger in the forward region than at midrapidity. We argue that this is a very specific prediction of the saturation framework, and we com…
This paper investigates the configurational entropic content of hadron-nucleus collisions. Hadron multiplicities and Au nuclei are employed to compute the critical points of the configurational entropy as a function of the saturation scale in deep inelastic scatterings, in QCD. The results match phenomenological data to the precision of 0.39%.
We show that gluon saturation gives rise to a strong modification of the scaling in both the nuclear mass number $A$ and the virtuality $Q^2$ of the vector meson production cross-section in exclusive deep-inelastic scattering off nuclei. We present qualitative analytic expressions for how the scaling exponents are modified as well as quantitative predictions that can be tested at an Electron-Ion Collider.
In high density QCD the hadron production stems from decay of mini-jets that have the transverse momenta of the order of the saturation scale. It is shown in this paper that this idea is able to describe in a unique fashion both the inclusive hadron production for \sqrt{s} \geq 546 GeV including the first data from LHC and the deep inelastic scattering at HERA. Recently reported data from ALICE, CMS and ATLAS including inclusive charged-hadron transverse-momentum and multiplicity distribution in pp collisions are well described in our approach. We provide predictions for the upcoming LHC measu…
The properties of mesonic resonances can be calculated in terms of the low-energy coefficients of chiral perturbation theory (chiPT) by extending unitarized chiPT to higher energies. On the other hand these low-energy coefficients can be calculated in two different models, namely (i) by assuming resonance saturation and (ii) within a constituent quark model. By matching the expressions of the two models combined with the results of unitarized chiPT and the Weinberg sum rules the properties of vector and axial-vector mesons can be calculated in the combined large-N_c and chiral limit.
If known, the spectrum of heavy-hadron molecules will be a key tool to disentangle the nature of the exotic states that are being discovered in experiments. Here we argue that the general features of the molecular spectrum can be deduced from the idea that the short-range interaction between the heavy hadrons is effectively described by scalar and vector meson exchange, i.e. the $σ$, $ω$ and $ρ$ mesons. By means of a contact-range theory where the couplings are saturated by the aforementioned light mesons we are indeed able to postdict the $X(3872)$ (as a $D^* \bar{D}$ molecule) from the three…
Through an analysis of diffractive vector meson production, we show that the proton appears quite dense to a small size probe at present HERA energies. This means that saturation effects are already important.
The exclusive vector meson production cross section is one of the most promising observables to probe the high energy regime of the QCD dynamics. In particular, the squared momentum transfer ($t$) distributions are an important source of information about the spatial distribution of the gluons in the hadron and about fluctuations of the color fields. In this paper we complement previous studies on exclusive vector meson photoproduction in hadronic collisions presenting a comprehensive analysis of the $t$ - spectrum measured in exclusive $ρ$, $ϕ$ and $J/Ψ$ photoproduction in $pp$ and $PbPb$ col…
We modified the gluon saturation model by rescaling the momentum fraction according to saturation momentum and introduced the Cooper-Frye hydrodynamic evolution to systematically study the pseudo-rapidity distributions of final charged hadrons at different energies and different centralities for Au-Au collisions in relativistic heavy-ion collisions at BNL Relativistic Heavy Ion Collider (RHIC). The features of both gluon saturation and hydrodynamic evolution at different energies and different centralities for Au-Au collisions are investigated in this paper.
Deep inelastic scattering at low x can be described by essentially only two fitted parameters. The interpretation of J/Psi photoproduction in terms of the gluon structure function is elaborated upon.
We discuss the recent claim that hadron multiplicities measured at RHIC energies are directly described in terms of gluon degrees of freedom fixed from the initial conditions of central heavy ion collisions. The argument is based on the parton saturation scenario expected to be valid at high parton densities and on the assumption of conserved gluon number. Alternatively we conjecture that "bottom-up" equilibration before hadronization modifies this picture, due to nonconservation of the number of gluons.
We investigate hadrons and direct photon production in pp and pA collisions at the energies of RHIC and LHC within the color-dipole approach employing various saturation models. We show that greatest sensitivity to saturation effects is reached at very forward rapidities for pp collisions at LHC (\sqrt{s}=14 TeV). The ratio of direct-photon to pion production can be about 20-10 (at η=7-8). Therefore, direct photon production at forward rapidities should provide a rather clean probe. We calculate the rapidity dependence of the invariant cross-section and find some peculiar enhancement at forwar…
RHIC experiments have recently measured the azimuthal correlation function of forward di-hadrons. The data show a disappearance of the away-side peak in central d+Au collisions, compared to p+p collisions, as was predicted by saturation physics. Indeed, we argue that this effect, absent at mid-rapidity, is a consequence of the small-x evolution into the saturation regime of the Gold nucleus wave function. We show that the data are well described in the Color Glass Condensate framework.
We demonstrate that rapidity separated di-hadron spectra in high multiplicity proton-proton collisions at the LHC can be quantitatively described by a combination of BFKL and saturation dynamics. Based on these results, we predict the systematics of di-hadron spectra in proton-nucleus collisions at the LHC.
The meson production cross sections are estimated considering photon-photon interactions in hadron - hadron collisions at CERN LHC energies. We consider a large number of mesons with photon-photon partial decay width well constrained by the experiment and some mesons which are currently considered as hadronic molecule and glueball candidates. Our results demonstrate that the experimental analysis of these states is feasible at CERN - LHC.
An addendum to our previous papers in Phys. Lett. B539 (2002) 46 and Phys. Lett. B502 (2001) 51, contributed to the CERN meeting "First data from the LHC heavy ion run", March 4, 2011
A study of saturation effects in two-hard-scale hadronic processes such as Mueller-Navelet jets is presented. The cross-sections are expressed in the dipole framework while saturation is implemented via an extention of the Golec-Biernat and Wusthoff model. The transition to saturation is found to be more abrupt than in gamma*-gamma* cross-sections. Observables with a potentially clear saturation signal are proposed.
Following recent predictions that the geometric scaling properties of deep inelastic scattering data in inclusive gamma*-p collisions are expected also in exclusive diffractive processes, we investigate the diffractive production of vector mesons. Using analytic results in the framework of the BK equation at non-zero momentum transfer, we extend to the non-forward amplitude a QCD-inspired forward saturation model including charm, following the theoretical predictions for the momentum transfer dependence of the saturation scale. We obtain a good fit to the available HERA data and make predictio…
We use recent results for the gamma*L -> rhoL and gamma*T -> rhoT impact factors, computed in the impact parameter representation within the collinear factorization scheme, to get predictions for the polarized cross-sections sigmaT and sigmaL of the diffractive leptoproduction of the rho meson at high energy. In this approach the helicity amplitude is a convolution of the scattering amplitude of a color dipole with a target, together with the virtual gamma wave function and with the first moments of the rho meson wave function (in the transverse momentum space), given by the distribution ampli…
The recent results in \sqrt{s}=2.76 TeV Pb+Pb collisions at the Large Hadron Collider (LHC) reported by the ALICE collaboration shows that the power-law energy-dependence of charged hadron multiplicity in Pb+Pb collisions is significantly different from p+p collisions. We show that this different energy-dependence can be explained by inclusion of a strong angular-ordering in the gluon-decay cascade within the Color-Glass-Condensate (or gluon saturation) approach. This effect is more important in nucleus-nucleus collisions where the saturation scale is larger than 1 GeV. Our prescription gives …
In this paper the optimal unitarity lower bound on logarithmic slope of the diffraction peak is investigated. It is shown that the unitarity lower bound is just the optimal logarithmic slopes predicted by the principle of least distance in space of states. A systematic tendency towards the saturation of the most forward-peaked limit is observed from all the available experimental data of all principal hadron-hadron (e.g., antiproton-proton, proton-proton, kaon-proton, pion-proton) scatterings practically at all laboratory momenta.
The forthcoming LHC measurements in proton-nucleus (pA) collisions at forward rapidities can discriminate between the color glass condensate (CGC) and alternative approaches including standard collinear factorization one. We report some of our recent predictions based on gluon saturation/CGC formalism for pA collisions at the LHC including the charged hadron multiplicity distribution, the nuclear modification factor for single inclusive hadron and prompt photon production, and the azimuthal angle correlation of the semi-inclusive hadron-photon production.
As Glauber has shown in 1959, the spin-flip phenomena caused by the conventional spin-orbit interaction do vanish in the scattering off heavy, strongly absorbing nuclei. On the other hand, the origin of the s-channel helicity nonconservation (SCHNC) in diffractive DIS is of the origin different from simple spin-orbit interaction, and here we demonstrate that SCHNC in vector meson production survives strong absorption effects in nuclear targets. The intranuclear absorption often discussed in terms of the saturation effects introduces a new large scale $Q_A^2$ into the calculation of diffractive…
We demonstrate the QCD factorization for inclusive hadron production in $pA$ collisions in the saturation formalism at one-loop order, with explicit calculation of both real and virtual gluon radiation diagrams. The collinear divergences associated with the incoming parton distribution of the nucleon and the outgoing fragmentation function of the final state hadron, as well as the rapidity divergence with small-$x$ dipole gluon distribution of the nucleus are factorized into the splittings of the associated parton distribution and fragmentation functions and the energy evolution of the dipole …
We calculate the cross section for diffractive hadron production in deep inelastic scattering off heavy nuclei in the framework of gluon saturation/color glass condensate. We analyze the kinematic region of the future Electron-Ion Collider. We argue that coherent and incoherent diffractive channels are very sensitive to the structure of the nuclear matter at low $x$. This expresses itself in a characteristic dependence of the cross sections on rapidity and transverse momentum of the produced hadron and on the nuclear weight. We also discuss dependence on the scattering angle and argue that bot…
We study saturation effects in the production of dijets in p-p and p-Pb collisions using the framework of high energy factorization. We focus on central-forward jet configurations, which allow for probing gluon density at low longitudinal momentum fraction. We find significant suppression of the central-forward jet decorrelations in p-Pb compared to p-p, which we attribute to saturation of gluon density in nuclei.
We confront saturation-based results for diffractive $ψ(2s)$ and $ρ$ production at HERA and $J/ψ$ photoproduction with all available data including recent ones from HERA, ALICE and LHCb, finding a good agreement. We show that the $t$-distribution of differential cross-section of photoproduction of vector mesons offers a unique opportunity to discriminate among saturation and non-saturation models. This is due to emergence of a pronounced dip (or multiple dips) in the $t$-distribution of diffractive photoproduction of vector mesons at relatively large, but potentially accessible $|t|$ that can …
There are generally two types of Wick contractions in lattice QCD calculations of a correlation function --- connected and disconnected ones. The disconnected contribution is difficult to calculate and noisy, thus it is often neglected. In the context of studying tetraquarks, hadronic molecules and meson-meson scattering, we show that whenever there are both connected and singly disconnected contractions, the singly disconnected part gives the leading order contribution, and thus should never be neglected. As an explicit example, we show that information about the scalar mesons sigma, f0(980),…
We provide a universal expression of cross sections for the exclusive vector meson production and Deeply Virtual Compton Scattering (DVCS) in photon-proton and photon-nucleus interactions based on the geometric scaling phenomenon. The theoretical parameterization based on the scaling property depends only on the single variable $τ_A = Q^2/Q_{\mathrm{sat}}^2$, where the saturation scale, $Q_{\mathrm{sat}}$, drives the energy dependence and the corresponding nuclear effects. This phenomenological result describes all available data from DESY-HERA for $ρ,\,ϕ,\,J/ψ$ production and DVCS measurement…
First results on charged hadron transverse momentum spectra in pp collisions obtained by the CMS Collaboration at LHC were analyzed in z-scaling approach. The first LHC data confirm z-scaling. The saturation regime of the scaling function psi(z) observed in pp and antp-pp interactions at lower energy sqrt s = 19-1960 GeV is verified. The saturation of psi(z) for charged hadrons is found down to z=0.05 at the highest energy sqrt s = 2360 GeV reached till now at colliders. A microscopic scenario of hadron production is discussed in connection with search for new signatures of phase transitions i…
In this paper we analyse the exclusive vector meson photoproduction in the recent run using Xenon-ions at energy of 5.44 TeV performed by the Large Hadron Collider. We focus on the ultraperipheral collisions and provide theoretical predictions for coherent and incoherent cross sections within the color dipole approach and gluon saturation framework. The rapidity distribution is investigated in both cases and comparison to other approaches available at literature is done. We show that the expected yields are enough to perform reliable cross section measurements for light mesons as $ρ^0$ and $ϕ$…
We perform the first next-to-leading order computation of the $γ^{(*)} \to V$ ($ρ, ϕ, ω$) impact factor in the QCD shockwave approach and in the most general kinematics. This paves the way to the very first quantitative study of high-energy nucleon and nucleus saturation beyond the leading order, in various processes to be measured in $ep$, $eA$, $pp$ and $pA$ collisions at existing and future colliders.
We extend the saturation models a la Golec-Biernat and Wusthoff to cross-sections of hard processes initiated by virtual-gluon probes separated by large rapidity intervals at hadron colliders. We derive their analytic expressions and apply them to physical examples, such as saturation effects for Mueller-Navelet forward jets. By comparison to gamma*-gamma* cross-sections we find a more abrupt transition to saturation. We propose to study observables with a potentially clear saturation signal and to use heavy vector and flavored mesons as alternative hard probes to forward jets.
We analyze the light-flavor particle mass spectra and show that in the region up to ~1.8GeV the Hagedorn temperature for baryons is about 30% smaller than for mesons, reflecting the fact that the number of baryon states grows more rapidly with the mass. We also show that the spectra are well reproduced in a model where hadrons are compound objects of quanta, whose available number increases with mass. The rapid growth of number of hadronic states is a combinatorial effect. We also point out that an upper limit on the excitation energy of these quanta results in a maximum number of hadron state…
Probing Saturation Effect in Heavy Meson Pair Correlation in Forward $pA$ Collisions
Three Gorges Tourism Polytechnic College（三峡旅游职业技术学院）；École polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院，巴黎理工学院）；Shandong University（山东大学）；The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）
Experimental data on inclusive cross sections of the hadrons produced in high energy proton-(anti)proton collisions are analyzed in the z-scaling approach. Saturation of the scaling function PSI(z) for z<0.1 (low transverse momenta) was found. The first results on charged hadron spectra in pp collisions obtained by the CMS Collaboration at the LHC have confirmed the saturation down to the value of z=0.05. The CMS data on neutral K-meson production at s^{1/2}=7 TeV extend the saturation region even to a lower value of z=0.002 in the new energy domain. A microscopic scenario of hadron production…
We consider pp, dAu and AuAu production of photons at RHIC energies, and PbPb collisions at LHC energy. We show that the inclusive spectrum of photons in the transverse momentum range of 1 GeV < pT <= 4 GeV satisfies geometric scaling. Geometric scaling is a property of hadronic interactions predicted by theories of gluon saturation, and expresses rates in terms of dimensionless ratios of the transverse momentum to saturation momentum. We show excellent agreement with geometric scaling with the only input being the previously measured dependence of the saturation momentum upon Bjorken x and ce…
It is already known from phenomenological studies that in exclusive deep-inelastic scattering off nuclei there appears to be a scaling behavior of vector meson production cross section in both nuclear mass number, $A$, and photon virtuality, $Q^{2}$, which is strongly modified due to gluon saturation effects. In this work we continue those studies in a realistic setup based upon using the Monte Carlo event generator Sar{\em t}re. We make quantitative predictions for the kinematics of the Electron-Ion Collider, focusing on this $A$ and $Q^{2}$ scaling picture, along with establishing a small re…
We study coherent and incoherent diffractive hadron production in high energy quarkonium--heavy nucleus collisions as a probe of the gluon saturation regime of QCD. Taking this process as a model for pA collisions, we argue that the coherent diffractive gluon production, in which the target nucleus states intact, exhibits a remarkable sensitivity to the energy, rapidity and atomic number dependence. The incoherent diffractive gluon production is less sensitive to the details of the low-x dynamics but can serve as a probe of fluctuations in the color glass condensate. As a quantitative measure …
We confront soft Pomeron and gluon saturation models with the first LHC data on inclusive hadron production. We claim that while the first type of models are not able to describe some part of the LHC data, the Colour-Glass-Condensate (gluon saturation) approach gives an adequate description of the data. Here, we compare our published predictions with the recently available 7 TeV data. We firmly believe that if further experimental measurements confirm that the gluon saturation works, it will be a major discovery.
Nuclear structure and saturation effects from diffractive vector meson production
University of Jyväskylä（于韦斯屈莱大学）；Helsinki Institute of Physics（赫尔辛基物理研究所）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Wayne State University（韦恩州立大学）；Central China Normal University（华中师范大学）
The diffractive vector meson photoproduction with hadron dissociation in coherent hadron-hadron interactions at LHC energies is studied assuming that the color singlet $t$-channel exchange carries large momentum transfer. We estimate the rapidity distribution and total cross section for the processes $pp \rightarrow p V X$ and $PbPb \rightarrow Pb V X$ ($V = ρ$ or $Υ$) considering the non-forward solution of the BFKL equation at high energy and large momentum transfer. Our results indicate that the experimental identification of these processes can be feasible at the LHC.
We investigate $ρ$ vector meson production in $ep$ collisions at HERA with leading neutrons in the dipole formalism. The interaction of the dipole and the pion is described in a mixed-space approach, in which the dipole-pion scattering amplitude is given by the Marquet-Peschanski-Soyez saturation model, which is based on the travelling wave solutions of the nonlinear Balitsky-Kovchegov equation. We estimate the magnitude of the absorption effects and compare our results with a previous analysis of the same process in full coordinate space. In contrast with this approach, the present study lead…
Equal time, point to point correlation functions for spatially separated meson currents are calculated with respect to a variational construct for the ground state of QCD. With exact calculations, vector, axial vector and scalar channels show qualitative agreement with the phenomenological predictions, where as pseudoscalar channel does not. However, the pseudoscalar correlator, when approximated by saturating with intermediate one pion states agrees with results obtained from spectral density functions parametrised by pion decay constant and $<\bar ψψ>$ value obtained from chiral perturbation…
Saturation models -- colour glass condensate and string percolation -- impose a strict relation between the average transverse momentum, <P_T>, and the rapidity particle densities, dn/dy. By combining this relation with an appropriate evolution equation for dn/dy, and imposing energy-momentum conservation, we obtain a fair description of data, for generic AB collisions (hadron-hadron, hadron-nucleus and nucleus-nucleus) at all rapidities and (high) energies. Predictions are given for the LHC.
We study the transverse spectra of hadrons in nearly central $AA$ collisions at RHIC and LHC in a broad transverse momentum range Low-$p_T$ spectra are calculated by using boost-invariant hydrodynamics with initial energy and net-baryon densities from the EKRT pQCD+saturation model. High-$p_T$ spectra are obtained from pQCD jet calculation including the energy loss of the parton in the matter prior to its fragmentation to final hadrons.
In this paper we study leading neutron production in photon - hadron interactions which take place in $pp$ and $pA$ collisions at large impact parameters. Using a model that describes the recent leading neutron data at HERA, we consider exclusive vector meson production in association with a leading neutron in $pp/pA$ collisions at RHIC and LHC energies. The total cross sections and rapidity distributions of $ρ$, $ϕ$ and $J/Ψ$ produced together with a leading neutron are computed. Our results indicate that the study of these processes is feasible and that it can be used to improve the understa…
The scattering cross sections of charm mesons with hadrons such as the pion, rho meson, and nucleon are studied in an effective Lagrangian. In heavy ion collisions, rescattering of produced charm mesons by hadrons affects the invariant mass spectra of both charm meson pairs and dileptons resulting from their decays. These effects are estimated for heavy ion collisions at SPS energies and are found to be significant.
The upcoming p+Pb run at the LHC will probe the nuclear gluon distribution at very small Bjorken x (from $x \sim 10^{-4}$ at mid-rapidity down to $x \sim 10^{-6}$ in the proton fragmentation region) and will allow to test approaches based on parton saturation. Here, we present the predictions of the KLN model for hadron multiplicities and multiplicity distributions in p+Pb collisions at a center-of-mass energy of 4.4 TeV. We also compare the model to the existing pp, dA and AA data from RHIC and LHC.
We study the production of $J/ψ$ vector mesons as a function of charged hadron multiplicity in p+p and p+Pb collisions at LHC energies. We employ the color glass condensate framework, using running coupling Balitsky-Kovchegov evolved dipole amplitudes, to compute gluon and $c\bar{c}$-pair production. We use fragmentation functions to obtain charged hadrons, and explore two different hadronization schemes for the $J/ψ$: non-relativistic quantum chromodynamics and the improved color evaporation model. In our framework, event-by-event multiplicity fluctuations of both hadrons and $J/ψ$ are driven…
